Modeling soybean growth: A mixed model approach

The evaluation of plant and animal growth, separately for genetic and environmental effects, is necessary for genetic understanding and genetic improvement of environmental responses of plants and animals. We propose to extend an existing approach that combines nonlinear mixed-effects model (NLMEM) and the stochastic approximation of the Expectation-Maximization algorithm (SAEM) to analyze genetic and environmental effects on plant growth. These tools are widely used in many fields but very rarely in plant biology. During model formulation, a nonlinear function describes the shape of growth, and random effects describe genetic and environmental effects and their variability. Genetic relationships among the varieties were also integrated into the model using a genetic relationship matrix. The SAEM algorithm was chosen as an efficient alternative to MCMC methods, which are more commonly used in the domain. It was implemented to infer the expected growth patterns in the analyzed population and the expected curves for each variety through a maximum-likelihood and a maximum-a-posteriori approaches, respectively. The obtained estimates can be used to predict the growth curves for each variety. We illustrate the strengths of the proposed approach using simulated data and soybean plant growth data obtained from a soybean cultivation experiment conducted at the Arid Land Research Center, Tottori University. In this experiment, plant height was measured daily using drones, and the growth was monitored for approximately 200 soybean cultivars for which whole-genome sequence data were available. The NLMEM approach improved our understanding of the determinants of soybean growth and can be successfully used for the genomic prediction of growth pattern characteristics.Author summary: Nonlinear models are useful for modeling animal and plant growth; however, their parameters are influenced by both genetic and environmental factors. If the same model can be applied to data with different genetic and environmental factors by allowing parameter variations, it can be used to understand, predict, and control the genetic and environmental influences of growth models based on parameter variation. In this study, we propose a statistical method based on nonlinear mixed-effects modeling. The simulation and real data analysis results show that the proposed method was effective in modeling the growth of genetically different soybean varieties under different drought conditions. The usefulness of the proposed method is expected to increase, as high-throughput measurements provide growth data for a large number of genotypes in various environments.